Roles of the Graphing Calculator
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Keith
Jan 17, 2008, 2:24:24 PM1/17/08
to MthEd608Winter2008
In what ways and to what extent do the roles discussed in Doerr and
Zangor (2000) capture your own experience using graphing calculators?
Do you think that some roles should be more encouraged or less
encouraged in mathematics classrooms?
Zangor (2000) capture your own experience using graphing calculators?
Do you think that some roles should be more encouraged or less
encouraged in mathematics classrooms?
Rachelle
Jan 18, 2008, 2:15:56 PM1/18/08
to MthEd608Winter2008
I was very impressed with the calculator use described in this
article. In my own experience, calculators were rarely (if ever) used
in such meaningful ways or for facilitating discussion. In high
school, I used a calculator as a computational tool, visualizing tool,
and checking tool. However, in using a calculator in these three ways,
my calculator use was generally not as rich as the uses described in
the paper. For example, I used a calculator as a computational tool,
but rarely with such meaning attached to the numbers as was described
in the article. Similarly, I used the calculator as a checking tool in
the trivial sense and not to check conjectures or explore phenomena. I
generally enjoyed using the calculator as a visualization tool
privately but never in small groups or in a whole-class discussion. I
never used a calculator as a transformational tool and only used it as
a data collection and analysis tool briefly in my undergraduate
technology class.
In light of my own shallow experience with calculators and the
impressive calculator use put forth in the article, I think more
emphasis in classrooms should be put on using calculators as a
transformational tool. The possibilities for doing mathematically
worthwhile tasks are greatly increased when the focus can move away
from repetitive computation and toward justification and
interpretation. To me, this is the most important tool the calculator
can be. I'm not sure how I feel about using the calculator as a data
collection and analysis tool, and I would love more insight (if anyone
has any comments!). For the other three tools, I think they should be
used and emphasized, but the focus must be on meaningful uses and not
simply the shallow uses from my experience.
article. In my own experience, calculators were rarely (if ever) used
in such meaningful ways or for facilitating discussion. In high
school, I used a calculator as a computational tool, visualizing tool,
and checking tool. However, in using a calculator in these three ways,
my calculator use was generally not as rich as the uses described in
the paper. For example, I used a calculator as a computational tool,
but rarely with such meaning attached to the numbers as was described
in the article. Similarly, I used the calculator as a checking tool in
the trivial sense and not to check conjectures or explore phenomena. I
generally enjoyed using the calculator as a visualization tool
privately but never in small groups or in a whole-class discussion. I
never used a calculator as a transformational tool and only used it as
a data collection and analysis tool briefly in my undergraduate
technology class.
In light of my own shallow experience with calculators and the
impressive calculator use put forth in the article, I think more
emphasis in classrooms should be put on using calculators as a
transformational tool. The possibilities for doing mathematically
worthwhile tasks are greatly increased when the focus can move away
from repetitive computation and toward justification and
interpretation. To me, this is the most important tool the calculator
can be. I'm not sure how I feel about using the calculator as a data
collection and analysis tool, and I would love more insight (if anyone
has any comments!). For the other three tools, I think they should be
used and emphasized, but the focus must be on meaningful uses and not
simply the shallow uses from my experience.
CJ
Jan 21, 2008, 9:52:46 PM1/21/08
to MthEd608Winter2008
Sometimes when I am typing on here I can't see the cursor . . . does
that happen to anyone else?
I have used graphing calculators more as a teacher than as a student.
It has actually been really neat as I have learned about different
types of functions (inverse trig functions, logarithms, etc) to
actually understand why the calculator gives me an error message. In
that sense, using calculators for computation has helped to emphasize
the existence of widespread definitions for functions, and the
explanation of the definitions usually causes me or my students to go
back and think about the definition as they consider what if? (Like
for example, if the inverse sine of 2 were defined, what kind of
triangle would I have to draw to show what is going on?) I am not
sure that I completely understand what it means to use the calculator
as a transformational tool, but it seems to mean that you can take the
focus away from time-consuming tasks to focus on generalizing the
results of those tasks. I think perhaps an example might be
investigating patterns in repeating decimal forms of rational
numbers . . . you could get them via long division, but once you did
you might not be able to see the patterns as you compare 1/11 to 2/11
and so forth. But maybe it's not the pattern but the process that
should be emphasized. Anyway, up to this point I have only talked
about things that could be done with a non-graphing calculator. I have
used CBRs with my students, and have observed how they adjust what
they do to make the data say what they want. Personally, I have used
graphs to ensure that I have found all of the solutions to an equation
on an interval, which may be a combination of visualization and
checking . . .
As far as encouraging and discouraging roles, I think it always
depends on what you want to accomplish. I feel like often calculators
are useful in helping us raise our level of mathematical inquiry
without getting bogged down in the details of plotting and computing.
The five roles described here seem like they can all be useful towards
that end. I really liked how the teacher kind of had a technology
skepticism, and how her students picked up on it and refused to
blindly accept whatever the calculator told them. It's also
interesting to note the authors conclusions about using calculators as
a private device. After we played with Diffy last week, I kind of
wondered if it would have been better or worse if we had been forced
to share computers as we worked together. What do you guys think?
Also, if someone wants to respond to my post, they can help me to
better understand the whole "transformational idea." Thanks.
that happen to anyone else?
I have used graphing calculators more as a teacher than as a student.
It has actually been really neat as I have learned about different
types of functions (inverse trig functions, logarithms, etc) to
actually understand why the calculator gives me an error message. In
that sense, using calculators for computation has helped to emphasize
the existence of widespread definitions for functions, and the
explanation of the definitions usually causes me or my students to go
back and think about the definition as they consider what if? (Like
for example, if the inverse sine of 2 were defined, what kind of
triangle would I have to draw to show what is going on?) I am not
sure that I completely understand what it means to use the calculator
as a transformational tool, but it seems to mean that you can take the
focus away from time-consuming tasks to focus on generalizing the
results of those tasks. I think perhaps an example might be
investigating patterns in repeating decimal forms of rational
numbers . . . you could get them via long division, but once you did
you might not be able to see the patterns as you compare 1/11 to 2/11
and so forth. But maybe it's not the pattern but the process that
should be emphasized. Anyway, up to this point I have only talked
about things that could be done with a non-graphing calculator. I have
used CBRs with my students, and have observed how they adjust what
they do to make the data say what they want. Personally, I have used
graphs to ensure that I have found all of the solutions to an equation
on an interval, which may be a combination of visualization and
checking . . .
As far as encouraging and discouraging roles, I think it always
depends on what you want to accomplish. I feel like often calculators
are useful in helping us raise our level of mathematical inquiry
without getting bogged down in the details of plotting and computing.
The five roles described here seem like they can all be useful towards
that end. I really liked how the teacher kind of had a technology
skepticism, and how her students picked up on it and refused to
blindly accept whatever the calculator told them. It's also
interesting to note the authors conclusions about using calculators as
a private device. After we played with Diffy last week, I kind of
wondered if it would have been better or worse if we had been forced
to share computers as we worked together. What do you guys think?
Also, if someone wants to respond to my post, they can help me to
better understand the whole "transformational idea." Thanks.
Tenille
Jan 24, 2008, 5:11:23 PM1/24/08
to MthEd608Winter2008
I consider myself fortunate to have had high school teachers who not
only allowed, but encouraged, the use of graphing calculators in the
classroom. In fact, I've been using a graphing calculator since my
eighth-grade geometry class (I won't tell you how long ago that was,
but TI-83 was the new kid on the block). As I considered my
experiences with the graphing calculator, I was able to find a moment
when I used the calculator for each of the identified roles. For
example, I used the calculator to evaluate expressions (didn't
everyone?), check my answers (especially when I was working with
systems of equations or graphing), gather data on a bouncing ball's
height (this use is restricted to my college and teaching
experiences), visualize and interpret equations and data, and I think
perhaps slightly as a transformational tool (I remember my pre-
calculus teacher describing how in the past when she taught regression
she had to focus on computations and was restricted to linear
regression, but with the calculator we would be able to explore
exponential and quadratic regression as well and determine which best
described our data). Still, I probably used it primarily as a
computational, visualizing, and checking tool. However, I don't think
that my use of the graphing calculator was as mathematically rich as
was described in the article. Although my teachers encouraged us to
explore with the graphing calculator and not to accept it as an
authority, they never followed-up our explorations with a discussion.
I think that the absence of a mathematical discussion weakened the use
of the calculator in the classroom.
A wise college professor once told me that the answer to all questions
is "It depends" (Dr. Grimshaw, BYU Statistics). This brings me to the
second question posed: do you think that some roles should be more
encouraged or less encouraged in the mathematics classroom? I think
that all roles should be encouraged. Let me qualify that statement
with the following explanation. I think that within each role there
are varying degrees of mathematical thinking participated in by the
student. For example, in the visualizing role, the calculator can be
used to graph equations or it can be used to compare and contrast
different modes of function representations that can be used to solve
systems of equations. I think that the former use is qualitatively
different from the rich mathematical potential of the later. I also
think that the different roles of the calculator accomplish different
things mathematically. For example, the role of the calculator as a
computational tool seems to allow more opportunities for students to
develop their number sense, whereas the data collection and analysis
role seems to provide students with an opportunity to explore physical
phenomena mathematically. Thus I think that all roles should be
encouraged, with careful considerations concerning the depth and type
of mathematics the teacher wants the students to learn.
only allowed, but encouraged, the use of graphing calculators in the
classroom. In fact, I've been using a graphing calculator since my
eighth-grade geometry class (I won't tell you how long ago that was,
but TI-83 was the new kid on the block). As I considered my
experiences with the graphing calculator, I was able to find a moment
when I used the calculator for each of the identified roles. For
example, I used the calculator to evaluate expressions (didn't
everyone?), check my answers (especially when I was working with
systems of equations or graphing), gather data on a bouncing ball's
height (this use is restricted to my college and teaching
experiences), visualize and interpret equations and data, and I think
perhaps slightly as a transformational tool (I remember my pre-
calculus teacher describing how in the past when she taught regression
she had to focus on computations and was restricted to linear
regression, but with the calculator we would be able to explore
exponential and quadratic regression as well and determine which best
described our data). Still, I probably used it primarily as a
computational, visualizing, and checking tool. However, I don't think
that my use of the graphing calculator was as mathematically rich as
was described in the article. Although my teachers encouraged us to
explore with the graphing calculator and not to accept it as an
authority, they never followed-up our explorations with a discussion.
I think that the absence of a mathematical discussion weakened the use
of the calculator in the classroom.
A wise college professor once told me that the answer to all questions
is "It depends" (Dr. Grimshaw, BYU Statistics). This brings me to the
second question posed: do you think that some roles should be more
encouraged or less encouraged in the mathematics classroom? I think
that all roles should be encouraged. Let me qualify that statement
with the following explanation. I think that within each role there
are varying degrees of mathematical thinking participated in by the
student. For example, in the visualizing role, the calculator can be
used to graph equations or it can be used to compare and contrast
different modes of function representations that can be used to solve
systems of equations. I think that the former use is qualitatively
different from the rich mathematical potential of the later. I also
think that the different roles of the calculator accomplish different
things mathematically. For example, the role of the calculator as a
computational tool seems to allow more opportunities for students to
develop their number sense, whereas the data collection and analysis
role seems to provide students with an opportunity to explore physical
phenomena mathematically. Thus I think that all roles should be
encouraged, with careful considerations concerning the depth and type
of mathematics the teacher wants the students to learn.
Rachelle
Jan 28, 2008, 6:18:45 PM1/28/08
to MthEd608Winter2008
With your question about the transformational tool, I think you hit it
right on. Doerr and Zangor mention that the calculator can be used as
a transformational tool, "whereby tedious computational tasks [are]
transformed into interpretive tasks" (pp. 152-153). However, it might
be that the authors intended a wider range of possibilites than simply
generalizing the results of a task; the purposes could include
anything interpretive like "What does this mean?" or "How does this
relate to my real-life experiences?" I think the Diffy task we did
last time would be a decent example. Instead of focusing on our
subtraction skills, the computer program allowed us to quickly
experiment with a wide range of numbers and let us know if we didn't
subtract right. That way, we could shift the focus from the
computation of subtracting to the interpretive tasks of finding
patterns, making conjectures, and coming up with proofs. The
calculator is rich with possibilities for transforming tasks from
tedious and time-consuming to interpretive and meaningful.
> > encouraged in mathematics classrooms?- Hide quoted text -
>
> - Show quoted text -
right on. Doerr and Zangor mention that the calculator can be used as
a transformational tool, "whereby tedious computational tasks [are]
transformed into interpretive tasks" (pp. 152-153). However, it might
be that the authors intended a wider range of possibilites than simply
generalizing the results of a task; the purposes could include
anything interpretive like "What does this mean?" or "How does this
relate to my real-life experiences?" I think the Diffy task we did
last time would be a decent example. Instead of focusing on our
subtraction skills, the computer program allowed us to quickly
experiment with a wide range of numbers and let us know if we didn't
subtract right. That way, we could shift the focus from the
computation of subtracting to the interpretive tasks of finding
patterns, making conjectures, and coming up with proofs. The
calculator is rich with possibilities for transforming tasks from
tedious and time-consuming to interpretive and meaningful.
>
> - Show quoted text -
Janellie
Jan 29, 2008, 2:27:52 PM1/29/08
to MthEd608Winter2008
My personal experience using the graphing calculator has been very
limited. During my calculus and physics classes were the only times I
used a graphing calculator in high school. In calculus, we used the
calculator for mainly computational purposes. It was a fast way to do
things such as find the value of an integral. In a very limited and
trivial sense, we also used it for visualizing certain functions. In
the physics class, we did some data collection and analysis using the
CBL devices. We used the temperature probe, matched some time
distance graphs with the motion detector. We then transfered this
information onto a computer to use it to predict future behavior and
analyze data. We used the calculator to check our computational work,
but not necessarily to check each others' conjectures. As reported by
Doerr and Zangor (2000), I found that one limitation of the graphing
calculator was that it often led individuals to cease working together
and just follow their own path of inquiry. In my calculus class, this
was ok because we did not really work together with others in that
class anyway. In college, I have experienced more of the roles of
graphing calculators. These roles were used mainly in my teaching
with technology class and methods (377). Therein we used the graphing
calculator in all the proposed roles, but mainly transformational,
visualizing, and checking. In the teaching with technology class, we
also did a significant amount of data collection. I especially liked
a task we did that required us to model a step function using the
motion detector.
I appreciated that the teacher in this study used calculators in such
a way that promoted student understanding. She did not allow students
to just accept the calculator as an authority, but rather required the
students to interpret the results by creating mathematical meanings of
the numerical and graphical data. In this sense, I think all the
roles are important and educative in a mathematics classroom.
However, I do believe there must be a balance in all things. If one
just uses the calculator for computational purposes, they are not
harnessing the full power of the calculator and are limiting their own
ability to understand the mathematics. Each of these roles are good
to emphasize as long as they allow students to reason, justify,
conjecture, prove, and receive a relational understanding of the
mathematics.
A question I have is, how much does one have to use calculators in the
classroom so their students will become able enough to utilize all the
capabilities of the graphing calculator? It seems like in this paper,
the students used the calculator ALL the time in their classroom. Is
this too much, or not?
limited. During my calculus and physics classes were the only times I
used a graphing calculator in high school. In calculus, we used the
calculator for mainly computational purposes. It was a fast way to do
things such as find the value of an integral. In a very limited and
trivial sense, we also used it for visualizing certain functions. In
the physics class, we did some data collection and analysis using the
CBL devices. We used the temperature probe, matched some time
distance graphs with the motion detector. We then transfered this
information onto a computer to use it to predict future behavior and
analyze data. We used the calculator to check our computational work,
but not necessarily to check each others' conjectures. As reported by
Doerr and Zangor (2000), I found that one limitation of the graphing
calculator was that it often led individuals to cease working together
and just follow their own path of inquiry. In my calculus class, this
was ok because we did not really work together with others in that
class anyway. In college, I have experienced more of the roles of
graphing calculators. These roles were used mainly in my teaching
with technology class and methods (377). Therein we used the graphing
calculator in all the proposed roles, but mainly transformational,
visualizing, and checking. In the teaching with technology class, we
also did a significant amount of data collection. I especially liked
a task we did that required us to model a step function using the
motion detector.
I appreciated that the teacher in this study used calculators in such
a way that promoted student understanding. She did not allow students
to just accept the calculator as an authority, but rather required the
students to interpret the results by creating mathematical meanings of
the numerical and graphical data. In this sense, I think all the
roles are important and educative in a mathematics classroom.
However, I do believe there must be a balance in all things. If one
just uses the calculator for computational purposes, they are not
harnessing the full power of the calculator and are limiting their own
ability to understand the mathematics. Each of these roles are good
to emphasize as long as they allow students to reason, justify,
conjecture, prove, and receive a relational understanding of the
mathematics.
A question I have is, how much does one have to use calculators in the
classroom so their students will become able enough to utilize all the
capabilities of the graphing calculator? It seems like in this paper,
the students used the calculator ALL the time in their classroom. Is
this too much, or not?
Shawn
Jan 29, 2008, 5:28:31 PM1/29/08
to MthEd608Winter2008
The roles of a graphing calculator that were discussed in the article
describe well what can happen in a classroom when they are used.
Looking back at what I can remember about my math education, only a
few of the roles discussed can be compared. The first is the
calculator as a computational tool. I did use it to compute as many
things as I could. I didn't have issues with the parentheses and
symbols because my calculator had an equation editor which took care
of all that for you. The second role was using the calculator as a
transformational tool. I don't recall using it in any way like that,
which would have been neat. The third role was using it as a data
collection and analysis tool. I also didn't have a chance to collect
and analyzing data with it, but I know that it was great at collecting
and analyzing data from what I read in the manual. I would have liked
to try some experiments with it, but I didn't have the necessary
attachments required. The fourth role was using it as a visualizing
tool. I did use it to visualize function equations a lot. This was
one of the fun things for me. Finally, I also used the calculator as
a checking tool, perhaps too much so. I would check everything. I
remember in my first calculus class checking all my derivatives and
integrals because the calculator could do it all symbolically.
I think that all the roles of a calculator should be encouraged some
in the classroom. I'm really not sure if there are any roles that
shouldn't be encouraged. I have thought about what might happen if
one of the roles was encouraged less and then I come to conclude that
certain mathematical properties would be missed. There are advantages
and disadvangages with each role. It just depends if you are willing
to deal with the disadvantages to get the advantages.
describe well what can happen in a classroom when they are used.
Looking back at what I can remember about my math education, only a
few of the roles discussed can be compared. The first is the
calculator as a computational tool. I did use it to compute as many
things as I could. I didn't have issues with the parentheses and
symbols because my calculator had an equation editor which took care
of all that for you. The second role was using the calculator as a
transformational tool. I don't recall using it in any way like that,
which would have been neat. The third role was using it as a data
collection and analysis tool. I also didn't have a chance to collect
and analyzing data with it, but I know that it was great at collecting
and analyzing data from what I read in the manual. I would have liked
to try some experiments with it, but I didn't have the necessary
attachments required. The fourth role was using it as a visualizing
tool. I did use it to visualize function equations a lot. This was
one of the fun things for me. Finally, I also used the calculator as
a checking tool, perhaps too much so. I would check everything. I
remember in my first calculus class checking all my derivatives and
integrals because the calculator could do it all symbolically.
I think that all the roles of a calculator should be encouraged some
in the classroom. I'm really not sure if there are any roles that
shouldn't be encouraged. I have thought about what might happen if
one of the roles was encouraged less and then I come to conclude that
certain mathematical properties would be missed. There are advantages
and disadvangages with each role. It just depends if you are willing
to deal with the disadvantages to get the advantages.
Shawn
Jan 29, 2008, 5:41:11 PM1/29/08
to MthEd608Winter2008
I'm not sure I know the best answer for your question, but I think
that the best way to teach students to become proficient with their
calculator is to teach them how to find the answers to their questions
instead of just teaching them all the functions the calculator has one
at a time. You would want to teach them how to interact with the
calculator, but once they have that down, showing them the manual and
how to use it, along with some online resources, they can learn more
about it and try more things on their own that you would have time in
class to teach. This is how I've learned. Then you would want to
make yourself available if they get stuck or have questions.
that the best way to teach students to become proficient with their
calculator is to teach them how to find the answers to their questions
instead of just teaching them all the functions the calculator has one
at a time. You would want to teach them how to interact with the
calculator, but once they have that down, showing them the manual and
how to use it, along with some online resources, they can learn more
about it and try more things on their own that you would have time in
class to teach. This is how I've learned. Then you would want to
make yourself available if they get stuck or have questions.
Just Plain Wright
Jan 29, 2008, 6:49:51 PM1/29/08
to MthEd608Winter2008
I have never used a graphing calculator personally. I have read
through parts of the instruction book with a high school aged daughter
to try and help her use it for a homework assignment. I have picked
it up on several occasions and put it in a more secure location than
the floor, couch, kitchen table or bathroom counter.
I have witnessed elementary teachers using them during a three year
research project. I saw them use the calculators to create graphs
based upon the input from a CBR unit. I have watched them grapple
with the meaning of the graphs based upon changing the types of
graphs: distance/time, speed/time, etc. I have observed some well-
versed in the calculators capacity, working with others less
familiar. I have noticed the silence in a small group when there are
several using their calculators and the conversation that errupts when
the results are discussed.
My experience is limited. My interest is peaked. From a hypothetical
perspective, I value the verification of hand sketched graphing using
calculators early on. This would tend to magnify errors students are
making graphing. I also value the use of calculator based
exploration, once the basic hand methods are in place. Particularly
because many variations can be tested in a short amount of time. I am
certain that continuing to hand draw all graphs would be tedious and
less effective (particularly considering the potential for error) when
a desire to extend to graphing beyond quadratic equations.
through parts of the instruction book with a high school aged daughter
to try and help her use it for a homework assignment. I have picked
it up on several occasions and put it in a more secure location than
the floor, couch, kitchen table or bathroom counter.
I have witnessed elementary teachers using them during a three year
research project. I saw them use the calculators to create graphs
based upon the input from a CBR unit. I have watched them grapple
with the meaning of the graphs based upon changing the types of
graphs: distance/time, speed/time, etc. I have observed some well-
versed in the calculators capacity, working with others less
familiar. I have noticed the silence in a small group when there are
several using their calculators and the conversation that errupts when
the results are discussed.
My experience is limited. My interest is peaked. From a hypothetical
perspective, I value the verification of hand sketched graphing using
calculators early on. This would tend to magnify errors students are
making graphing. I also value the use of calculator based
exploration, once the basic hand methods are in place. Particularly
because many variations can be tested in a short amount of time. I am
certain that continuing to hand draw all graphs would be tedious and
less effective (particularly considering the potential for error) when
a desire to extend to graphing beyond quadratic equations.
CJ
Jan 29, 2008, 8:58:30 PM1/29/08
to MthEd608Winter2008
Thanks for your question, Janelle. I feel like I have to be the nay-
sayer here and jump on the opportunity to make the statement that my
experience makes me believe that you probably can use the calculator
too much. In trying to teach algebra to students that should already
know algebra, I linked their inability to solve an equation to their
inability to evaluate an expression which I linked to a lack of
understanding of the order of operations which I linked to, what else,
a graphing calculator. Maybe my logic is faulty, but the backwards/
forwards phenomena requires you to at least understand something about
the order of operation to get a decent answer using a scientific
(backwards) calculator or more basic calculators. The graphing
calculators (forwards), on the other hand, seem to take care of all
that stuff for you. There also seems to be a problem with plotting
functions. Many people seem to forget that a graph of a function is
really just a collection of points, and that they can always go back
to plotting points if they didn't memorize enough transformations or
basic shapes of graphs. Does having a machine that makes the graph for
you just further promote this forgetfulness phenomenon? Don't get me
wrong, I'm really not anti-technology. I am kind of reminding me of
those people who think that we should go back to using slide rulers to
force people to learn about logarithms. I don't know if that's decent
logic either. I've just noticed that people who know where all the
functions on a graphing calculator are do seem to use them a lot . . .
and I mean A LOT.
If you would like a sane response to your question, I recommend
Shawn's.
sayer here and jump on the opportunity to make the statement that my
experience makes me believe that you probably can use the calculator
too much. In trying to teach algebra to students that should already
know algebra, I linked their inability to solve an equation to their
inability to evaluate an expression which I linked to a lack of
understanding of the order of operations which I linked to, what else,
a graphing calculator. Maybe my logic is faulty, but the backwards/
forwards phenomena requires you to at least understand something about
the order of operation to get a decent answer using a scientific
(backwards) calculator or more basic calculators. The graphing
calculators (forwards), on the other hand, seem to take care of all
that stuff for you. There also seems to be a problem with plotting
functions. Many people seem to forget that a graph of a function is
really just a collection of points, and that they can always go back
to plotting points if they didn't memorize enough transformations or
basic shapes of graphs. Does having a machine that makes the graph for
you just further promote this forgetfulness phenomenon? Don't get me
wrong, I'm really not anti-technology. I am kind of reminding me of
those people who think that we should go back to using slide rulers to
force people to learn about logarithms. I don't know if that's decent
logic either. I've just noticed that people who know where all the
functions on a graphing calculator are do seem to use them a lot . . .
and I mean A LOT.
If you would like a sane response to your question, I recommend
Shawn's.
erin...@byu.edu
Jan 30, 2008, 10:24:04 PM1/30/08
to MthEd608Winter2008
I'm slightly confused by the question, but I assume that the "roles"
encompass more the "five patterns and modes of graphing calculator
tool use" that were discussed in the study, and so that's what I am
responding to!
Firstly, my own experience: in my high school we would "check-out"
graphing calculators from the school for the duration of an entire
year. I think we checked them out every year by 9th. Our senior year
we had these beautiful hp calculators that could do ridiculously
amazing things. In college, the only time I used a graphing
calculator is when we borrowed some for Math Ed 308 (or whatever one
is Teaching With Technology). All throughout my undergrad math
classes I just did stuff in my head/ on paper or whiteboards. I do
own a scientific calculator that I would use sometimes, but typically
I forgot to bring it to school while I did my homework... My
experience, therefore, in using calculators is that they serve
primarily to support the work one could do by hand. Don't get me
wrong, I have seen amazing things done with them while I was student
teaching and I definitely know that my perspective ought to be
expanded; my experience, however, is simply that they are good to help
with cumbersome computations or to let you see what the graph of a
particular function looks like (or how the graphs of multiple
functions compare), or to provide you with a table of values where you
can choose how large of increments you want the input to change...
Doeer and Zangor definitely discussed calculators as being
computational tools, visualizing tools, and checking tools. I didn't
really use a calculator as a data collection/analysis tool in the way
the authors discussed. Also, although I used the calculator to help
visualize functions, I did it mostly to help me see how a particular
function behaved outside of the small part that I could figure out
myself. The authors discussed it both in the way I did (to determine
the underlying structure of the function), and also in a way I didn't:
as a strategy to find equations that fit data sets.
I actually really like the primary roles/ functions of a graphing
calculator that I came to view it as. I do think I could be more
educated on other helpful uses for it, but i like that I am not
dependent on a graphing calculator and that I can reason through
problems on my own. I do think I could be more efficient if I knew
some more of the glorious things calculators can do, but again-
calculators should supplement what we know, not provide a foundation
(and it would be a very sandy foundation at that - definitely not one
built to withstand floods!). That would be, I think, making certain
assumptions about the calculator as being an authority... we all know
what happens when you assume anything.
encompass more the "five patterns and modes of graphing calculator
tool use" that were discussed in the study, and so that's what I am
responding to!
Firstly, my own experience: in my high school we would "check-out"
graphing calculators from the school for the duration of an entire
year. I think we checked them out every year by 9th. Our senior year
we had these beautiful hp calculators that could do ridiculously
amazing things. In college, the only time I used a graphing
calculator is when we borrowed some for Math Ed 308 (or whatever one
is Teaching With Technology). All throughout my undergrad math
classes I just did stuff in my head/ on paper or whiteboards. I do
own a scientific calculator that I would use sometimes, but typically
I forgot to bring it to school while I did my homework... My
experience, therefore, in using calculators is that they serve
primarily to support the work one could do by hand. Don't get me
wrong, I have seen amazing things done with them while I was student
teaching and I definitely know that my perspective ought to be
expanded; my experience, however, is simply that they are good to help
with cumbersome computations or to let you see what the graph of a
particular function looks like (or how the graphs of multiple
functions compare), or to provide you with a table of values where you
can choose how large of increments you want the input to change...
Doeer and Zangor definitely discussed calculators as being
computational tools, visualizing tools, and checking tools. I didn't
really use a calculator as a data collection/analysis tool in the way
the authors discussed. Also, although I used the calculator to help
visualize functions, I did it mostly to help me see how a particular
function behaved outside of the small part that I could figure out
myself. The authors discussed it both in the way I did (to determine
the underlying structure of the function), and also in a way I didn't:
as a strategy to find equations that fit data sets.
I actually really like the primary roles/ functions of a graphing
calculator that I came to view it as. I do think I could be more
educated on other helpful uses for it, but i like that I am not
dependent on a graphing calculator and that I can reason through
problems on my own. I do think I could be more efficient if I knew
some more of the glorious things calculators can do, but again-
calculators should supplement what we know, not provide a foundation
(and it would be a very sandy foundation at that - definitely not one
built to withstand floods!). That would be, I think, making certain
assumptions about the calculator as being an authority... we all know
what happens when you assume anything.
Janellie
Jan 31, 2008, 12:36:05 PM1/31/08
to MthEd608Winter2008
I would like to respond to Rachelle's question (statement) about the
calculator being used as a data collection and analysis tool. I think
this is the role of the calculator that I am most intrigued with. For
example, you can stick a temperature probe in water and the calculator
will collect the temperature at specified time intervals. Also, you
can measure light with another device. I think this allows students
to gather data quickly and focus more on the mathematics associated
with the data. One will not have to check the temperature every 2
minutes themselves. My favorite is the motion detector. We use this
feature to measure distance over time by gathering data from something
(or someone) that moves. We can talk about distance graphs, velocity
graphs, and acceleration graphs and how they are related to each
other. In Math Ed 308 we had to model the step function using motion
and a graphing calculator.
calculator being used as a data collection and analysis tool. I think
this is the role of the calculator that I am most intrigued with. For
example, you can stick a temperature probe in water and the calculator
will collect the temperature at specified time intervals. Also, you
can measure light with another device. I think this allows students
to gather data quickly and focus more on the mathematics associated
with the data. One will not have to check the temperature every 2
minutes themselves. My favorite is the motion detector. We use this
feature to measure distance over time by gathering data from something
(or someone) that moves. We can talk about distance graphs, velocity
graphs, and acceleration graphs and how they are related to each
other. In Math Ed 308 we had to model the step function using motion
and a graphing calculator.
Tenille
Jan 31, 2008, 2:45:31 PM1/31/08
to MthEd608Winter2008
I would like to thank Janelle (and Chris) for including questions in
their responses. I think we should all follow their example. Now I
am sure that some of you are probably silently swearing at me in your
heads as I suggest more work for each of us to do. So I will make it
a personal goal to ask more questions. I suppose this suggestion
comes from insights I have received as I have had the opportunity to
study the First Vision again in depth. I have learned through the
example of Joseph Smith the importance of asking questions in order to
get answers (see JS-H 1:10). But I digress . . .
As a teacher, I often asked myself the same question Janelle
suggested: how much time should we have our students spend using the
graphing calculator. I struggled to find the perfect balance,
incorporating calculator and non calculator days. I think that I may
have been wrong to do so. I agree that students need to be able to
function without a calculator, but I wonder if that can occur without
restricting the use of the calculator. For example, during my final
year of teaching I chose not to restrict my students' use of the
calculator during the graphing linear equations unit. Instead, I let
them play around with the calculator and graph the equations as often
as they would like. Eventually, most of the students decided that it
took more time to graph the linear equation on the calculator than it
did for them to draw the graph by hand. And what about the students
who continued to use the calculator to graph linear equations? I don't
think that it would have made a difference to them if I had not
allowed them to use the calulator at the beginning of the unit. As
for the Chris' suggestion that the calculator masks what it means for
a point to be a solution to the line and that the line is made up of
a collection of points . . . eventually students are going to ask how
the calculator graphs lines. Bingo!
Now you can talk about it and the students might actually care.
I think that if you want the students to use the calculator as more
than just a trivial computational tool, you have to have them interact
with the calculator a lot . . . and I mean A LOT! Luckily, I have
found that in this technology-savy age in which we live, students are
able to climb the learning curve relatively quickly and become more
adept at using the calulator than I am.
their responses. I think we should all follow their example. Now I
am sure that some of you are probably silently swearing at me in your
heads as I suggest more work for each of us to do. So I will make it
a personal goal to ask more questions. I suppose this suggestion
comes from insights I have received as I have had the opportunity to
study the First Vision again in depth. I have learned through the
example of Joseph Smith the importance of asking questions in order to
get answers (see JS-H 1:10). But I digress . . .
As a teacher, I often asked myself the same question Janelle
suggested: how much time should we have our students spend using the
graphing calculator. I struggled to find the perfect balance,
incorporating calculator and non calculator days. I think that I may
have been wrong to do so. I agree that students need to be able to
function without a calculator, but I wonder if that can occur without
restricting the use of the calculator. For example, during my final
year of teaching I chose not to restrict my students' use of the
calculator during the graphing linear equations unit. Instead, I let
them play around with the calculator and graph the equations as often
as they would like. Eventually, most of the students decided that it
took more time to graph the linear equation on the calculator than it
did for them to draw the graph by hand. And what about the students
who continued to use the calculator to graph linear equations? I don't
think that it would have made a difference to them if I had not
allowed them to use the calulator at the beginning of the unit. As
for the Chris' suggestion that the calculator masks what it means for
a point to be a solution to the line and that the line is made up of
a collection of points . . . eventually students are going to ask how
the calculator graphs lines. Bingo!
Now you can talk about it and the students might actually care.
I think that if you want the students to use the calculator as more
than just a trivial computational tool, you have to have them interact
with the calculator a lot . . . and I mean A LOT! Luckily, I have
found that in this technology-savy age in which we live, students are
able to climb the learning curve relatively quickly and become more
adept at using the calulator than I am.
Just Plain Wright
Jan 31, 2008, 6:28:47 PM1/31/08
to MthEd608Winter2008
Being a visual learner, I am grateful for teachers and tools that
provide an opportunity to see the mathematics. I am jealous of your
exposure to the graphing calculator as I have not had the same
experience. What I have found valuable is knowing the standard
equation form of familiar functions and conics. From these standard
forms I have tried to learn what manipulations of the standard form
will produce the graph I expect. This prediction tool cannot be lost
with introduction of the calclutor.
provide an opportunity to see the mathematics. I am jealous of your
exposure to the graphing calculator as I have not had the same
experience. What I have found valuable is knowing the standard
equation form of familiar functions and conics. From these standard
forms I have tried to learn what manipulations of the standard form
will produce the graph I expect. This prediction tool cannot be lost
with introduction of the calclutor.
erin...@byu.edu
Jan 31, 2008, 6:44:22 PM1/31/08
to MthEd608Winter2008
I think that proficiency in using the calculators is only possible
through experience. Verbal or written directions can only assist/
lead a student so far without them knowing the processes on their
own. How do students become competent in factoring or using the
quadratic formula, or artists become great artists by theory alone? i
do think there comes a time when students can use a graphing
calculator too much because i don't see how you can use it literally
all the time without becoming dependent on it... that's all (and I'm
sorry this was late, but i still wanted to post).
through experience. Verbal or written directions can only assist/
lead a student so far without them knowing the processes on their
own. How do students become competent in factoring or using the
quadratic formula, or artists become great artists by theory alone? i
do think there comes a time when students can use a graphing
calculator too much because i don't see how you can use it literally
all the time without becoming dependent on it... that's all (and I'm
sorry this was late, but i still wanted to post).
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